The Bucks, who have gutted their team and have plenty of cap space, are shaping up as the leading suitor for J.R. Smith.

But if Smith leaves the Knicks to get more bucks in Milwaukee, he will find himself in a rebuilding program. That’s the decision the Freehold, N.J., native, has to make.

Take less to stay with the hometown Knicks, who can offer a four-year, roughly $24 million contract — which comes to $6 million a season after yearly raises — or follow the “green’’ jerseys of Milwaukee or another under-the-cap club willing to make a four-year commitment. The market value is being set for him to get an offer of at least $7 million per year.

The Racine (Wis.) Journal Times reported a week ago the backcourt-challenged Bucks would make a run at Smith and are waiting until they come to an agreement with restricted free-agent point guard Brandon Jennings. The Suns also could make a play for Smith with their cap space, and a source said the Pistons have minimal interest.

The rate for Smith is rising. According to Yahoo! Sports, J.J. Redick got four years and $27 million in a sign-and-trade to the Clippers, and he’s not the league’s reigning Sixth Man. Aging shooting guard Kevin Martin signed a deal with the Timberwolves for $6.25 million a year and isn’t the player Smith is anymore. Both deals are similar to what the Knicks can offer Smith, but the Bucks are in position to significantly top it.

The Bucks sent away Redick in a multi-team deal that landed them two second-round picks. The club looks to be cleaning out its roster to give itself a chance at winning the 2014 lottery for Andrew Wiggins.

This week, Bucks shooting guard Monta Ellis turned down his $11.5 million option and became a free agent and Mike Dunleavy signed with the Bulls. The Bucks are desperate for offense. The question could become: Is Smith desperate for them?

* A Spanish-speaking website tweeted last night that the Knicks made Pablo Prigioni a two-year contract offer. The Knicks likely used a portion of their mini mid-level.

* Memo from Rome: Andrea Bargnani is happy to be out of Canada. Bargnani, who will join the Knicks after becoming a scapegoat with the Raptors, tweeted yesterday from Italy: “I am thrilled to become a New York Knick and look forward to becoming a part of their storied franchise.’’

Bargnani also thanked the Toronto organization and “his fans.’’ Those were dwindling in Toronto the past two seasons.

* SG/SF Richard Hamilton was released and could pique the Knicks’ interest for the vet’s minimum. … If the Knicks reacquire the rights to their 2012 Greek draft pick, Kostas Papanikolaou, they will have to go through Houston. The Blazers traded the Greek forward to the Rockets to obtain Thomas Robinson. The Knicks had made previous offers for Papanikolaou.